Machine learning has enjoyed astounding practical success in a wide range of applications in recent years-practical success that often hurries ahead of our theoretical understanding. The standard framework for machine learning theory assumes full supervision, that is, training data consists of correctly labeled iid examples from the same task that the learned classifier is supposed to be applied to. However, many practical applications successfully make use of the sheer abundance of data that is currently produced. Such data may not be labeled or may be collected from various sources. The focus of this thesis is to provide theoretical analysis of machine learning regimes where the learner is given such (possibly large amounts) of non-perfect training data. In particular, we investigate the benefits and limitations of learning with unlabeled data in semi-supervised learning and active learning as well as benefits and limitations of learning from data that has been generated by a task that is different from the target task (domain adaptation learning). For all three settings, we propose Probabilistic Lipschitzness to model the relatedness between the labels and the underlying domain space, and we discuss our suggested notion by comparing it to other common data assumptions.

A living city must exist at every scale - from the urban to the pedestrian; the development of the 21st century Instant City, however, does not allow for this multiplicity of scales. These cities emerge instead in a type of hyper-reality, driven by the pursuit of capital and power. In the frenzy to grow, the resulting urban condition is alienating - one devoid of human scale. Looking to modern Dubai as an example of the dehumanized city, this thesis explores the reinterpretation of a traditional bazaar as a tool to challenge this existing form of urbanism. By way of an intervention that exploits the connective potential of pedestrian infrastructure, the project seeks to add a layer of social and physical complexity to a ‘dead’ city.

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This dissertation establishes mathematical foundations for the properties exhibited by generalizations of cliques, as well as algorithms to find such objects in a network. Cliques are a model of an ideal group with roots in social network analysis. They have since found applications as a part of grouping mechanisms in computer vision, coding theory, experimental design, genomics, economics, and telecommunications among other fields. Because only groups with ideal properties form a clique, they are often too restrictive for identifying groups in many real-world networks. This motivated the introduction of clique relaxations that preserve some of the various defining properties of cliques in relaxed form. There are six clique relaxations that are the focus of this dissertation: s-clique, s-club, s-plex, k-core, quasi-clique, and k-connected subgraphs. Since cliques have found applications in so many fields, research into these clique relaxations has the potential to steer the course of much future research. The focus of this dissertation is on bringing organization and rigorous methodology to the formation and application of clique relaxations. We provide the first taxonomy focused on how the various clique relaxations relate on key structural properties demonstrated by groups. We also give a framework for how clique relaxations can be formed. This equips researchers with the ability to choose the appropriate clique relaxation for an application based on its structural properties, or, if an appropriate clique relaxation does not exist, form a new one. In addition to identifying the structural properties of the various clique relaxations, we identify properties and prove propositions that are important computationally. These assist in creating algorithms to find a clique relaxation quickly as it is immersed in a network. We give the first ever analysis of the computational complexity of finding the maximum quasi-clique in a graph. Such analysis identifies for researchers the appropriate set of computational tools to solve the maximum quasiclique problem. We further create a polynomial time algorithm for identifying large 2-cliques within unit disk graphs, a special class of graphs often arising in communication networks. We prove the algorithm to have a guaranteed 1=2-approximation ratio and finish with computational results.

Many chaotic and complicated systems cannot be analysed by traditional methods. In 1987 P.Bak, C.Tang, and K.A.Wiesenfeld developed a new concept called Self-Organised Criticality (SOC) to explain the behaviour of composite systems containing a large number of elements that interact over a short range. In general this theory applies to complex systems that naturally evolve to a critical state in which a minor event starts a chain reaction that can affect any number of elements in the system. It was later shown that many complex phenomena such as flux pinning in superconductors, dynamics of granular systems, earthquakes, droplet formation and biological evolution show signs of SOC. The dynamics of complex systems in nature often occurs in terms of punctuation, or avalanches rather than following a smooth, gradual path. Extremal dynamics is used to model the temporal evolution of many different complex systems. Specifically the Bak-Sneppen evolution model, the Sneppen interface depinning model, the Zaitsev flux creep model, invasion percolation, and several other depinning models. This thesis considers extremal dynamics at constant flux where M>1 smallest barriers are simultaneously updated as opposed to models in the limit of zero flux where only the smallest barrier is updated. For concreteness, we study the Bak-Sneppen (BS) evolution model [Phys. Rev. Lett. 71, 4083 (1993)]. M=1 corresponds to the original BS model. The aim of the present work is to understand analytically through mean field theory the random neighbour version of the generalised BS model and verify the results against the computer simulations. This is done in order to scrutinise the trustworthiness of our numerical simulations. The computer simulations are found to be identical with results obtained from the analytical approach. Due to this agreement, we know that our simulations will produce reliable results for the nearest neighbour version of the generalised BS model. Since the nearest neighbour version of the generalised BS model cannot be solved analytically, we have to rely on simulations. We investigate the critical behaviour of both versions of the model using the scaling theory. We look at various distributions and their scaling properties, and also measure the critical exponents accurately verifying whether the scaling relations holds. The effect of increasing from M=1 to M>1 is surprising with dramatic decrease in size of the scaling regime.

In this thesis I claim that dominant realist, interpretive and postmodern research methodologies, taken together, provide necessary but not sufficient tools for use within educational research. Understandings of material, social and linguistic worlds do not, in themselves, cater for teachers' pragmatic needs to consider (a) the social consequences of educational practices, both their own and those of the institutions within which they work, and (b) the complexity of teaching in a postmodern world. I draw on ideas from pragmatism, post-structuralism, critical pedagogy, complexity theory, reflective practice, and personal experience in order to invite the emergence (or social construction) of new phenomena: these I hope, may enable teachers and other educationalists to take a vibrant part in ongoing debates and actions concerning educational policy and practice. I argue that the assumption that educational theory can be applied in practice is flawed and needs to be replaced by theory which recognises the dynamic nature of theory-in-practice: all theory is data within practice. This is a late-career thesis written by a practitioner with an unusually broad experience of the New Zealand educational system. I argue that the purpose of theory is to guide practice, that practice must drive theory, and that theory and practice need to join together to focus on the consequences of planned actions. This is neo-pragmatism, but, as stated thus far, it is not enough for my purposes because it does not include a commitment to social justice. Praxis is a term which ties emancipatory political goals to theory-and-practice. I invite the construction of the understandings of praxitioner activities where collective praxis and individual praxis might co-emerge in the interests of social justice. I promote the expansion of fresh discourses through research into collective praxis within teaching and teacher education.

This thesis explores how the discourse of complexity thinking can be used to foster emergence in curriculum and practice-based research. The curriculum-related exploration focused specifically on games of chase as one facet of early childhood curriculum. It investigated using complexity thinking firstly, to occasion emergence (that is, create a new phenomenon) in children’s games of chase at an early childhood centre and secondly, to describe this emergence. The research-related exploration focused on creating an emergent methodology which is underpinned by complexity thinking. In this thesis report, I present a series of emergent curriculum-related phenomena that arose during the explorations, that is, an emergent game, a local curriculum theory for games of chase, the concepts of local curriculum theory, curriculum design and curriculum dynamics, and a curriculum vision. I also present an understanding of emergent methodology and two methodological innovations in the form of the Research Data Management System and the Visual Summary. This research involved taking the role of a volunteer teacher-researcher-curriculum designer at an early childhood centre to play games of chase with children. This role was informed by and contributed to a curriculum design that focused on designing the teaching and learning environment to occasion emergence in learning and curriculum. The games of chase curriculum contributed to children’s learning, my own learning and the general rhythm of life at the centre. The children learnt to distinguish between children who were playing and those who were not. They also learnt different ways to tag people in a game. In addition, the children and I developed a game playing routine before playing each game. This routine involved putting on tag belts, discussing what game we were playing and how we were going to play it. We played three different games of chase, starting with tag, followed by What is the time Mr(s) Wolf?, and finally the emergent game Big A, Little A. The stories of emergence are described in visual, descriptive and narrative texts organised into curriculum stories, teaching stories and children’s learning stories. Curriculum stories describe the activities that unfolded. Teaching stories present stories of teaching while learning stories are stories of children’s learning. These stories represent views of the enacted curriculum as activity, teaching and learning respectively. Taken together, the stories present a description of the curriculum dynamics that unfolded at the centre in relation to games of chase. This thesis shows that a local curriculum theory for games of chase at the centre emerged from the complex interactions of curriculum design and curriculum dynamics that unfolded at the centre. It also articulates the emergent concepts of local curriculum theory, curriculum design and curriculum dynamics using the language of complexity. This thesis also presents the local curriculum theory as a curriculum vision. This vision involves a shift in thinking about curriculum as either a set “course to be run” or the “path created in the running” (currere) to embracing curriculum as both “the space for running” and currere. It is a vision that values both children’s and teachers’ interests, focuses on teachers and children exploring depth and breadth of a curriculum domain together, enables teachers to follow, generate and sustain children’s interest in the explorations, and is generative, flexible and future-focused. This thesis conceptualises an emergent methodology as a methodology for emergence which (1) involves the researcher actively striving to foster emergence in research, (2) is brought forth in the interactions between the designed and enacted facets of methodology, (3) is local to a particular research project, and (4) emerges from the interactions of several related strategies. This thesis can be seen as an attempt to change the language game of curriculum by using the language of complexity throughout the thesis. In so doing, it not only enables the reader to talk about the discourse of complexity thinking, it also enables the reader to experience the discourse and the emergence of the curriculum-related phenomena and the methodological innovations that are the focus of this thesis. Finally, this thesis argues that using the discourse of complexity thinking in teaching and research can be enabling. It can enable the teacher and/or researcher to be creative, flexible and ethical within the constraints of his/her professional and personal life.

This dissertation investigates interactions between gender and number and gender and evaluative morphology in a sample of 100 African languages, and provides a method for assessing the role that these interactions play in the grammatical complexity of gender systems. The dissertation is organised around three research foci. First, the dissertation surveys patterns of interaction between gender and number along the following dimensions: exponence, syncretism, indexation, correlations in type of marking, and gender assignment. The study provides evidence for the possibility that nominal features are organised in a relevance hierarchy. In addition, the study shows that animacy and lexical plurality play a crucial role in the distribution of special patterns of plural indexation. The study also shows that pervasive indexation systems in the language sample always involve both gender and number. Finally, the study shows how gender assignment can be used as a means for encoding variation in the countability properties of nouns and noun phrases. Second, the dissertation surveys patterns of interaction between gender and evaluative morphology in the languages of the sample. Two types of interactions are found. The study shows that the distribution of the two types depends on three factors: the type of gender system, the number of gender distinctions and the possibility of assigning a noun to more than one gender. Third, the dissertation investigates the role that interactions of gender and number and gender and evaluative morphology play in the absolute complexity of gender. The study proposes a metric for gender complexity and uses this metric to compute complexity scores for the languages of the sample. The results suggest that the gender systems of the language sample lean toward high complexity, that genealogically related languages have the same or similar complexity scores, and that the distribution of the outliers can often be understood as the result of language contact.

A recent growth in textual analysis research in the accounting and finance literature relies heavily on context to draw conclusions about the readability or sentiment of the text under study. Yet the complexity of the text used in the financial disclosure is also relevant in evaluating readability and sentiment. Experimental results in this dissertation thesis show that a change in annual report complexity is associated with a change in the probability that a subject will comprehend the information being communicated in the disclosure. Specifically, increasing the complexity of an annual report disclosure dampens the probability that a subject will understand good news disclosures and accentuates the probability that a subject will understand bad news disclosures. Experimental results in this dissertation thesis also demonstrate that a change in annual report complexity is associated with a change in the probability that a subject will be optimistic about the nature of the news being communicated in the disclosure. Specifically, an increase in the complexity of an annual report disclosure reduces the probability that a subject will be optimistic about neutral news disclosures, decreases the probability that a subject will be optimistic about good news disclosures, and increases the probability that a subject will be optimistic about bad news disclosures. Further, experimental results show that subjects utilize the Financial Statements, Management's Discussion and Analysis, and Business Data sections of the annual report more frequently than the Notes to Financial Statements section of the annual report. These results should be of interest to regulators, public corporations, and readers of annual report disclosures.